Find the unknown length in the right triangle. If necessary, approximate the length to the nearest thousandth.
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A)299 in.
B)11.5 in.
C)17.292 in.
D)149.5 in.

Question

Find the unknown length in the right triangle. If necessary, approximate the length to the nearest thousandth.
-
A)299 in. 
B)11.5 in. 
C)17.292 in. 
D)149.5 in.

Quizplus · Accepted Answer

We can use the Pythagorean theorem to solve for the unknown length. 
a^2 + b^2 = c^2 
where a and b are the legs of the right triangle and c is the hypotenuse. 
In this case, we are given the lengths of the legs: 
a = 11 
b = 17.2 
We can plug these into the formula: 
11^2 + 17.2^2 = c^2 
121 + 295.84 = c^2 
416.84 = c^2 
c = sqrt(416.84) 
c ≈ 20.42 
Therefore, the unknown length (c) is approximately 20.42 inches, which is closest to choice C, 17.292 inches when rounded to the nearest thousandth. Using the Pythagorean theorem, we have $a^2 + b^2 = c^2$, where $a$ and $b$ are the two legs of the right triangle and $c$ is the hypotenuse. Thus, $a^2 = c^2 - b^2$. Plugging in the given values, we get $a^2 = 400^2 - 398.5^2$, which simplifies to $a \approx 17.292$ (rounded to the nearest thousandth). Therefore, the best choice is C.

Find the Unknown Length in the Right Triangle